{"cells":[{"cell_type":"markdown","metadata":{"id":"vNmpcGOqYIS7"},"source":["# The Curse of Unrolling\n","\n","Given an implicit function defined based on the solution to a (quadratic convex) optimization problem\n","\n","$$\n","q(\\theta) =\n","\\left \\{\n","\\text{solve}\n","\\;\n","\\arg \\min_x\n","f(x, \\theta)\n","\\right \\}\n","=: x^*\n","$$\n","\n","with\n","\n","$$\n","f(x, \\theta) = \\frac{1}{2} \\theta x^2 - bx \\qquad \\theta, x \\in \\mathbb{R}\n","$$\n","\n","and its approximation by gradient descent\n","\n","$$\n","\\tilde{q}(\\theta;x^{[0]}, \\eta, T)\n","=\n","\\left \\{\n","x^{[T]}=\\phi^T(x^{[0]})\n","\\;\n","\\text{with}\n","\\;\n","\\phi(x^{[t]})=x^{[t]}- \\eta\\frac{\\partial f}{\\partial x}\\bigg|_{x=x^{[t]}, \\theta}\n","\\right \\} = x^{[T]}\n","$$\n","\n","how does the **Jacobian suboptimality** converge based on the number of iterations taken in the gradient descent approximation\n","\n","$$\n","\\left| \\left|\n","\\frac{\\partial x^{[t]}}{\\partial \\theta}\n","-\n","\\frac{\\partial x^*}{\\partial \\theta}\n","\\right| \\right|_F\n","$$"]},{"cell_type":"markdown","metadata":{},"source":["This notebook is based on the paper \"The Curse of Unrolling: Rate of Differentiating through Optimization\" by Scieur et al. (2022): [https://arxiv.org/abs/2209.13271](https://arxiv.org/abs/2209.13271)"]},{"cell_type":"code","execution_count":1,"metadata":{"executionInfo":{"elapsed":8,"status":"ok","timestamp":1678896094419,"user":{"displayName":"Felix Köhler","userId":"04567813699266562054"},"user_tz":-60},"id":"wJLyT4VlAbc0"},"outputs":[],"source":["import jax\n","import jax.numpy as jnp\n","import matplotlib.pyplot as plt"]},{"cell_type":"code","execution_count":2,"metadata":{},"outputs":[],"source":["plt.style.use(\"dark_background\")"]},{"cell_type":"code","execution_count":3,"metadata":{},"outputs":[],"source":["B_VALUE = 0.0"]},{"cell_type":"code","execution_count":4,"metadata":{},"outputs":[],"source":["def inner_objective(x, theta):\n","    return 0.5 * theta * x**2 - B_VALUE * x"]},{"cell_type":"code","execution_count":5,"metadata":{},"outputs":[],"source":["def inner_objective_arg_optimum(theta):\n","    return B_VALUE / theta"]},{"cell_type":"code","execution_count":6,"metadata":{},"outputs":[{"data":{"text/plain":["<matplotlib.legend.Legend at 0x7cc9e0752350>"]},"execution_count":6,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["x_range = jnp.linspace(-2, 2, 100)\n","for theta in [0.1, 0.5, 1.0, 2.0]:\n","    inner_objective_values = inner_objective(x_range, theta)\n","    plt.plot(x_range, inner_objective_values, label=\"theta: \" + str(theta))\n","    plt.vlines(inner_objective_arg_optimum(theta), -0.3, 4.0, color=\"grey\", linewidth=3, linestyles=\"dashed\")\n","plt.grid()\n","plt.xlim(-2.0, 2.0)\n","plt.ylim(-0.3, 4.0)\n","plt.legend()"]},{"cell_type":"code","execution_count":7,"metadata":{},"outputs":[],"source":["def gd_step(x_prev, theta, learning_rate):\n","    x_next = x_prev - learning_rate * jax.grad(inner_objective, argnums=0)(x_prev, theta)\n","    return x_next\n","\n","def optimize_gd(theta, init=0.5, learning_rate=0.1, num_iter=1000):\n","    \"\"\"\n","    Performs optimization via gradient descent and returns the full history of\n","    iterates.\n","    \"\"\"\n","    def scan_fn(x_prev, _):\n","        x_next = gd_step(x_prev, theta, learning_rate)\n","        return x_next, x_next\n","    \n","    _, x_history = jax.lax.scan(scan_fn, init, None, length=num_iter)\n","\n","    x_history_with_init = jnp.concatenate([jnp.array([init]), x_history])\n","\n","    return x_history_with_init"]},{"cell_type":"code","execution_count":8,"metadata":{},"outputs":[],"source":["THETA = 0.05"]},{"cell_type":"code","execution_count":9,"metadata":{},"outputs":[],"source":["gd_iterates = optimize_gd(THETA)"]},{"cell_type":"code","execution_count":10,"metadata":{},"outputs":[{"data":{"text/plain":["Array([0.5       , 0.4975    , 0.4950125 , ..., 0.00336051, 0.00334371,\n","       0.00332699], dtype=float32)"]},"execution_count":10,"metadata":{},"output_type":"execute_result"}],"source":["gd_iterates"]},{"cell_type":"code","execution_count":11,"metadata":{},"outputs":[{"data":{"text/plain":["(1001,)"]},"execution_count":11,"metadata":{},"output_type":"execute_result"}],"source":["gd_iterates.shape"]},{"cell_type":"code","execution_count":12,"metadata":{},"outputs":[],"source":["solution_suboptimality = jnp.abs(gd_iterates - inner_objective_arg_optimum(THETA))\n","loss_suboptimality = jnp.abs(\n","    # EDIT: In the video, the row below incorrectly used\n","    # `solution_suboptimality` instead of `gd_iterates`. Thanks to @YOak_ML for\n","    # spotting this. (It does not change the curves and the conclusion here,\n","    # because the analytical optimizer is `0`, given the choice of `B_VALUE`.)\n","    inner_objective(gd_iterates, THETA)\n","    -\n","    inner_objective(inner_objective_arg_optimum(THETA), THETA)\n",")"]},{"cell_type":"code","execution_count":13,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["plt.plot(solution_suboptimality, label=\"Solution suboptimality\")\n","plt.plot(loss_suboptimality, label=\"loss suboptimality\")\n","plt.yscale(\"log\")\n","plt.xlabel(\"Optimization iteration\")\n","plt.ylabel(\"Suboptimality\")\n","plt.legend()\n","plt.grid()"]},{"cell_type":"code","execution_count":14,"metadata":{},"outputs":[],"source":["iterate_jacobian = jax.jacfwd(optimize_gd, argnums=0)(THETA)"]},{"cell_type":"code","execution_count":15,"metadata":{},"outputs":[{"data":{"text/plain":["(1001,)"]},"execution_count":15,"metadata":{},"output_type":"execute_result"}],"source":["iterate_jacobian.shape"]},{"cell_type":"code","execution_count":16,"metadata":{},"outputs":[],"source":["exact_jacobian = jax.jacfwd(inner_objective_arg_optimum)(THETA)"]},{"cell_type":"code","execution_count":17,"metadata":{},"outputs":[],"source":["jacobian_suboptimality = jnp.abs(\n","    iterate_jacobian - exact_jacobian\n",")"]},{"cell_type":"code","execution_count":18,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["plt.plot(solution_suboptimality, label=\"Solution suboptimaliy\")\n","plt.plot(loss_suboptimality, label=\"Loss suboptimality\")\n","plt.plot(jacobian_suboptimality, label=\"Jacobian Suboptimality\")\n","plt.yscale(\"log\")\n","plt.legend()\n","plt.xlabel(\"Optimization Iteration\")\n","plt.ylabel(\"Suboptimality\")\n","plt.grid()"]},{"cell_type":"markdown","metadata":{},"source":["### Explaining the result\n","\n","Here in our case the inner objective is\n","\n","$$f(x, \\theta) = \\frac{1}{2}\\theta x^2$$\n","\n","As a consequence, the update rule for gradient descent is\n","\n","$$\\phi(x)=x - \\eta\\frac{\\partial f}{\\partial x} = x - \\eta\\theta x = (1 -\\eta \\theta) x$$\n","\n","Evaluating this auto-regressively gives the recurrence\n","\n","$$x^{[t]}=\\phi^t(x^{[0]})=\n","(1 - \\eta \\theta)^tx^{[0]}$$\n","\n","And for the Jacobian\n","\n","$$\\frac{\\partial x^{[t]}}{\\partial \\theta}=-\\eta t(1-\\eta \\theta)^{t-1}x^{[0]}$$\n","\n","The analytical optimizer of our problem is easy\n","\n","$$\\frac{\\partial f}{\\partial x}=\\theta x \\overset{!}{=}0 \\quad \\iff\n","\\quad x^*=0 \\quad\n","\\implies \\frac{\\partial x^*}{\\partial \\theta}=0$$\n","\n","As such the Jacobian suboptimality is just\n","\n","$$\\left| \\left|\n","\\frac{\\partial x^{[t]}}{\\partial \\theta} - \\frac{\\partial x^*}{\\partial \\theta}\n","\\right| \\right|\n","=\n","\\left|\n","\\eta t(1-\\eta \\theta)^{t-1}x^{[0]}\n","\\right|$$\n","\n","Plugging in our values, $\\eta=0.1$, $\\theta=0.05$ and $x^{[0]}=0.5$\n","\n","$$\\left| \\left|\n","\\frac{\\partial x^{[t]}}{\\partial \\theta} - \\frac{\\partial x^*}{\\partial \\theta}\n","\\right| \\right|\n","=\n","\\left|\n","0.05 t(0.995)^{t-1}\n","\\right|$$"]},{"cell_type":"code","execution_count":19,"metadata":{},"outputs":[],"source":["t_range = jnp.arange(1, 500)\n","linear_sequence = 0.05 * t_range\n","exponential_sequence = 0.995 ** (t_range - 1 )"]},{"cell_type":"code","execution_count":20,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["plt.scatter(t_range[:30], linear_sequence[:30]*exponential_sequence[:30], label=\"product\")\n","plt.scatter(t_range[:30], linear_sequence[:30], label=\"linear\")\n","plt.scatter(t_range[:30], exponential_sequence[:30], label=\"exponential\")\n","plt.legend()\n","plt.grid()"]},{"cell_type":"code","execution_count":21,"metadata":{},"outputs":[{"data":{"text/plain":["<matplotlib.legend.Legend at 0x7cc9b9665fc0>"]},"execution_count":21,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["plt.scatter(t_range, linear_sequence * exponential_sequence, label=\"product\")\n","plt.grid()\n","plt.legend()"]},{"cell_type":"markdown","metadata":{},"source":["As such the length of the burn-in period will be\n","\n","$$t_{burn-in} ≈ \\frac{1}{\\kappa}$$\n","\n","$\\kappa$ here just is $\\theta = 0.05$, hence $t_{burn-in} \\approx 200$"]},{"cell_type":"markdown","metadata":{},"source":["Feel free to play around with the parameters:\n","\n","- $\\eta$: the learning rate\n","- $b$: the linear term in the objective\n","- $x_{init}$: the initial value for the optimization\n","- $\\dots$\n","\n","Ultimately, you will notice the \"Curse of Unrolling\""]},{"attachments":{"Screenshot from 2024-03-31 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"}},"cell_type":"markdown","metadata":{},"source":["![Screenshot 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